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Blizzard [7]
3 years ago
7

How many distinct proper subsets are there of the set N = {10, 50, 63, 15, 40, 55}?

Mathematics
1 answer:
ASHA 777 [7]3 years ago
8 0

Answer:

Proper\ Subset = 63

Step-by-step explanation:

Given

N = \{10, 50, 63, 15, 40, 55\}

Required

Determine the proper subsets

This is calculated by:

Proper\ Subset = 2^n - 1

<em>Where n is the number of elements in the set.</em>

In this case,

n = 6

So:

Proper\ Subset = 2^n - 1

Proper\ Subset = 2^6 - 1

Proper\ Subset = 64- 1

Proper\ Subset = 63

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In the figure, ray OB bisects ∠TOY.
Levart [38]

<u><em>Answer:</em></u>

∠BOY = 38°

<u><em>Explanation:</em></u>

<u>From the diagram, we can note that:</u>

m∠TOY = m∠TOB + m∠BOY ...................> equation I

We are given that ray OB bisects the angle

<u>Therefore:</u>

m∠TOB = m∠BOY

<u>Substitute in equation I:</u>

m∠TOY = m∠TOB + m∠TOB = 2m∠TOB ............> equation II

<u>We are given that:</u>

m∠TOY = 8x-36

m∠TOB = x+24

<u>Substitute with the givens in equation II and solve for x:</u>

m∠TOY = 2m∠TOB

8x - 36 = 2(x + 24)

2(4x-18) = 2(x+24)

4x - 18 = x + 24

3x = 42

x = 14

<u>This means that:</u>

m∠TOB = x + 24 = 14 + 24 = 38°

<u>Since </u>

m∠TOB = m∠BOY

<u>Therefore:</u>

m∠BOY = 38°

<u>Check:</u>

m∠TOY = 8x - 36 = 8(14) - 36 = 76° which is twice m∠TOB

Hope this helps :)

8 0
4 years ago
A partial sum of an arithmetic sequence is given. Find the sum.
Nezavi [6.7K]

Answer:

72.3

Step-by-step explanation:

Given that:

The arithmetic sequence:

\sum \limits ^{14}_{k=0} (3 + 0.26k)

The first term of the sequence a_0 = 3 since k = 0

i.e (3 + 0.26(0)) = 3

The last term of the sequence a_{14} = 6.64

i.e (3+ 0.26(14)

= (3 + 3.64)

= 6.64

Total no of terms = 15 i.e from 0 to 14

∴

The partial sum of the arithmetic sequence = \dfrac{Total \ no \ of \ terms }{2}  \times (a_o+a_{15})}

=\dfrac{15 }{2}  \times (3+6.64)}

= 72.3

3 0
3 years ago
Simplify the expression.
user100 [1]
Ur answer is. 5 y^2+4y+14 because I went through it in class
6 0
3 years ago
Rewrite n square root x square m using rational expression
Anna35 [415]

Step-by-step explanation:

\sqrt[?]{?}

x m

5 0
3 years ago
The baby lions at the zoo are growing. For the first 4 months, they eat 10 ounces of food per day. Every month after that, the a
denpristay [2]

Answer:

48.3

Step-by-step explanation:

6 0
2 years ago
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